Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Classical State Detection Using Quantum State Tomography

Kim Fook Lee, Prem Kumar

Abstract

We present a model to detect a classical state mixed with an idler photon from a polarization-entangled pair. A weak coherent light with a well-defined polarization, matched in wavelength to the idler photon, is injected into the idler channel. Quantum state tomography is then performed on both the classically mixed idler photon and its entangled signal partner. The reconstructed state is modeled as a combination of an $X-$quantum state and a classical-quantum (CQ) state. In this framework, the weak coherent light acts as a measurement apparatus performing a local polarization measurement on the idler channel, thereby inducing a classical state. The density matrix of the classical state is identified via algorithmic analysis of the diagonal and off-diagonal elements of the reconstructed density matrix. This approach could advance techniques for classical-quantum coexistence in networking applications$\,-\,$such as quantum wrapping$\,-\,$as well as future quantum key distribution protocols based on the coexistence of weak coherent states and entangled photon states.

Classical State Detection Using Quantum State Tomography

Abstract

We present a model to detect a classical state mixed with an idler photon from a polarization-entangled pair. A weak coherent light with a well-defined polarization, matched in wavelength to the idler photon, is injected into the idler channel. Quantum state tomography is then performed on both the classically mixed idler photon and its entangled signal partner. The reconstructed state is modeled as a combination of an quantum state and a classical-quantum (CQ) state. In this framework, the weak coherent light acts as a measurement apparatus performing a local polarization measurement on the idler channel, thereby inducing a classical state. The density matrix of the classical state is identified via algorithmic analysis of the diagonal and off-diagonal elements of the reconstructed density matrix. This approach could advance techniques for classical-quantum coexistence in networking applicationssuch as quantum wrappingas well as future quantum key distribution protocols based on the coexistence of weak coherent states and entangled photon states.

Paper Structure

This paper contains 23 sections, 28 equations, 2 figures.

Table of Contents

  1. 1. Introduction
  2. 2. Results
  3. 2.1 Procedure to identify Operator $\mathcal{B}$
  4. 2.2 Detection of Classical State H
  5. 2.3 Detection of Classical State A
  6. 2.4 Detection of Classical State L
  7. 2.5 The relative strength between $p^{f}_{11}$ and $p^{f}_{14}$
  8. 2.6 Quantum Discord
  9. 3. Discussion
  10. 4. Conclusion
  11. 5. Methods
  12. 5.1 The Reconstructed Density Matrix of the measured final $X-$ States
  13. 5.2 The $2(\mathcal{E'}\rho_{w}(H)\mathcal{E'}^{\dagger})$ with the $\mathcal{E'}=(\mathcal{B=H})\bigotimes\mathcal{I}$
  14. 5.3 The $\mathcal{E}$ and $\mathcal{E'}$ for $\mathcal{B}=V$
  15. 5.4 The $2(\mathcal{E'}\rho_{w}(A)\mathcal{E'}^{\dagger})$ with the $\mathcal{E'}=(\mathcal{B=A})\bigotimes\mathcal{I}$
  16. ...and 8 more sections

Figures (2)

  • Figure 1: A counter-propagating scheme is used to generate two-photon polarization entangled photon pairs. The polarization state of the weak coherent light is prepared in free-space and then mixed with the idler photon through a DWDM. Transmission from port R to port C of the DWDM provides 23 dB of attenuation for weak coherent light at 1561 nm. The classically mixed idler photon and the signal photon are analyzed by two spatially separate polarization analyzers ($\rm{PA_{s,i}}$). HWP; Half-wave plate. QWP; Quarter-wave plate. PBS; polarization beam splitter. SPD; Single photon detector.
  • Figure 2: (a). The plot of $y =\frac{p\cdot x -2\cdot p}{p\cdot x -p-1}$ for the classical state $A$ whether $a <0$ or $a > 0$. The same plot applies to the classical state $D$ for the negative values of $a < \frac{p\cdot x}{4\cdot x -4.0}$. (b). The plot of $a =\frac{p\cdot x}{4\cdot x -4.0}$. The top region is in the range $\frac{p\cdot x}{4\cdot x -4}<a<0$ for the classical state $A$. The bottom region is in the range $a < \frac{p\cdot x}{4\cdot x -4}$ for the classical state $D$.